Title: Toric multisections and curves in rational surfaces.
Abstract: Trisections were introduced by Gay and Kirby. They are a natural generalization of a Heegaard splitting of a 3-manifold. We can encode every knot in a 3-manifold, using Heegaard diagrams, and analogously we can encode surfaces in 4-manifolds using trisection diagrams. In this talk, I will describe multisections of embedded surfaces in 4-manifolds admitting effective torus actions. A simply-connected 4-manifold admits a genus one multisection if and only if it admits an effective torus action. I will also talk about the algebraic topology of genus one multisected 4-manifolds.
This is a joint work with Islambouli, Lambert-Cole, and Meier